The authors consider operators of the form           in a bounded domain of     where         are nonsmooth Hörmander's vector fields of step   such that the highest order commutators are only Hölder continuous. Applying Levi's parametrix method the authors construct a local fundamental solution   for   and provide growth estimates for   and its first derivatives with respect to the vector fields. Requiring the existence of one more derivative of the coefficients the authors prove that   also possesses second derivatives, and they deduce the local solvability of  , constructing, by means of  , a solution to   with Hölder continuous  . The authors also prove      estimates on this solution.